Network model for the numerical solution of groundwater flow. Application to partially penetrating retaining structures in geotechnical engineering

Based on the network simulation method, a precise numerical model is designed for the 2‐D groundwater flow in porous and isotropic aquifers. If a partially penetrating impervious barrier exists, groundwater will flow downstream circumventing the underground structure. The network model is solved free code. Thanks to the powerful mathematical calculation algorithms implemented in is this type of codes, the provided solutions are quite precise for a relatively small grid size, with practically negligible computing times. The proposed model is applied to illustrative problems, providing hydraulic isopotentials and stream lines, showing that as the dam penetration depth increases the hydraulic gradient downstream decreases, thus reducing the risk of hydraulic failure.We would like to thank the Séneca Foundation for the support given to this research and for the scholarships awarded to María Encarnación Martínez Moreno to carry out her doctoral thesis

Numerical simulation of seepage maps under dams with sheet piles on their ends

Seepage maps formed by both stream and equipotential lines, emerging under dams with sheet piles on their ends, can be determined by simulating the Laplace conjugate equations using a numerical technique such as the network method. Based on these maps, engineers can immediately deduce the amount of water circulating under the structure and design the sheet piles depth to safe values that allow to limit risks such as siphoning or erosion of the base of the dam. For a fix depth of the upstream sheet pile, seepage maps are shown for different configurations of the downstream sheet pile, in a 2D scenario with finite depth and with large extensions both upstream and downstream of the dam.We would like to thank the Séneca Foundation for the support given to this research, thanks to the scholarship awarded to María Encarnación Martínez Moreno to carry out her doctoral thesis

On the Nondimensionalization Process in Complex Problems: Application to Natural Convection in Anisotropic Porous Media

The nondimensionalization of the equations governing a given problem is a direct, relatively easy, and low-cost way to provide interesting information, the dimensionless groups that rule the problem and define its final patterns of solution. In complex problems, however, this technique frequently does not provide the precise and complete set of monomials we are looking for. The use of discrimination in the process of nondimensionalization, the detailed application of which is explained in this paper, always leads to a minimum set of parameters, which, separately, determine the solution of the problems. In addition, the physical meaning and order of magnitude of these discriminated monomials are also provided by the discrimination. The technique is applied to the coupled problem of natural convection between horizontal plates heated from below, containing an anisotropic porous medium

Solución numérica de problemas de elasticidad bidimensional, basados en la formulación directa de navier o en funciones potenciales mediante el método de redes: el programa EPSNET_10

[SPA] La complejidad de resolución de los problemas elastostáticos, enunciados en forma general por la Ecuación de Navier, normalmente requiere el uso de técnicas numéricas tales como Elementos Finitos. El principal objetivo de las formulaciones alternativas en términos de funciones potenciales ha sido la obtención de soluciones analíticas. Sólo algunos casos, en los que son aplicables funciones sencillas tales como Airy y Prandtl, se han resuelto numéricamente en términos de potenciales. En esta tesis se presenta la aplicación del método de simulación por redes a la solución numérica de problemas de elasticidad 2D planteados con la formulación de Navier o con funciones potenciales; centrándose en los potenciales de Papkovich-Neuber y formulaciones derivadas, por eliminación de alguna de las funciones potenciales, para los que no se han encontrado soluciones numéricas hasta la fecha. Tras presentar los fundamentos teóricos de esta memoria (Capítulo 2) y discutir las condiciones de completitud y unicidad de la representación de Papkovich-Neuber, se profundiza en las condiciones adicionales para la unicidad numérica (Capítulo 3), cuestión aún sin resolver en toda su extensión. En este sentido, se proponen nuevas condiciones de unicidad numérica para algunas de las formulaciones en potenciales aplicables a casos bidimensionales. En particular, para los potenciales de Boussinesq, se aportan condiciones más sencillas y alternativas a las propuestas hasta la fecha, únicas según Tran-Cong. El diseño de modelos en red y la implementación de las condiciones físicas de contorno, tanto para la formulación de Navier como para la formulación en potenciales, se explica en el capítulo 4. Se ha elaborado un programa en Matlab con interfaz gráfica, EPSNET_10, para la generación de modelos en red, simulación en PSpice y representación gráfica de resultados. Su funcionamiento y las opciones de usuario que contiene se explican en el capítulo 5. En los capítulos 6 y 7 se presentan las aplicaciones a problemas enunciados bajo los dos tipos de formulaciones, Navier y en potenciales, respectivamente. Para verificar la fiabilidad de los modelos propuestos se comparan sus resultados con las soluciones analíticas, cuando existen, o con las de otros métodos numéricos de uso común en elasticidad. [ENG] The complexity of solving elastostatic problems, defined by the Navier equation, usually requires numerical tools such as Finite Element. The main aim of the alternative formulations in terms of potential functions has been to get analytical solutions. Only certain cases, where straightforward functions as Airy and Prandtl can be applied, have been solved numerically in terms of potential. The network simulation method is applied in this PhD Thesis on the numerical solution of 2D elastostatic problems based either in Navier formulation or in potential formulation, focusing on the Papkovich-Neuber potentials and derived solutions, by deleting some of the potential functions, for which no numerical solutions have been investigated up to day. After exposing the theoretical bases of this memory (Chapter 2) and discussing the completeness and uniqueness conditions of the Papkovich-Neuber solution, the additional conditions required for the numerical solution are studied (Chapter 3). This question is still a matter of active interest in the research literature. In this sense, new additional conditions are proposed for some potential solutions applicable to 2D problems. In the case of the Boussinesq solution, the conditions proposed up to day, unique according to Tran-Cong, can be specified in alternative forms, even more simple. The design of the network models as well as the implementation of the physical boundary conditions, for both Navier and potential formulations, is explained in Chapter 4. Software has been developed in Matlab programming language, with graphical interface, EPSNET_10. This contains the routines for the network design, simulation in PSpice and data treatment for the graphical result representation. Its performance and multiple user options are explained in Chapter 5. Applications to problems defined by Navier and potential formulations are presented in Chapters 5 and 6, respectively. The reliability of the proposed models are verified by comparison between its results and analytical solutions, if they exist, or otherwise with standard numerical methods solutions, currently used in elasticity.[ENG] The complexity of solving elastostatic problems, defined by the Navier equation, usually requires numerical tools such as Finite Element. The main aim of the alternative formulations in terms of potential functions has been to get analytical solutions. Only certain cases, where straightforward functions as Airy and Prandtl can be applied, have been solved numerically in terms of potential. The network simulation method is applied in this PhD Thesis on the numerical solution of 2D elastostatic problems based either in Navier formulation or in potential formulation, focusing on the Papkovich-Neuber potentials and derived solutions, by deleting some of the potential functions, for which no numerical solutions have been investigated up to day. After exposing the theoretical bases of this memory (Chapter 2) and discussing the completeness and uniqueness conditions of the Papkovich-Neuber solution, the additional conditions required for the numerical solution are studied (Chapter 3). This question is still a matter of active interest in the research literature. In this sense, new additional conditions are proposed for some potential solutions applicable to 2D problems. In the case of the Boussinesq solution, the conditions proposed up to day, unique according to Tran-Cong, can be specified in alternative forms, even more simple. The design of the network models as well as the implementation of the physical boundary conditions, for both Navier and potential formulations, is explained in Chapter 4. Software has been developed in Matlab programming language, with graphical interface, EPSNET_10. This contains the routines for the network design, simulation in PSpice and data treatment for the graphical result representation. Its performance and multiple user options are explained in Chapter 5. Applications to problems defined by Navier and potential formulations are presented in Chapters 5 and 6, respectively. The reliability of the proposed models are verified by comparison between its results and analytical solutions, if they exist, or otherwise with standard numerical methods solutions, currently used in elasticity.Universidad Politécnica de CartagenaPrograma de doctorado en Tecnologías Industriale

Bibliography of Lewis Research Center technical publications announced in 1987

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1987. All the publications were announced in the 1987 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-3)

Papers from the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES) are presented. The papers discuss current research in the general field of inverse, semi-inverse, and direct design and optimization in engineering sciences. The rapid growth of this relatively new field is due to the availability of faster and larger computing machines

Solución numérica de problemas de oxidación mediante el método de simulación por redes

[SPA] En esta tesis se aplica el método de simulación por redes a la solución numérica de problemas de oxidación química estudiando todas las vertientes del fenómeno, en particular los procesos de reacción química que tienen lugar en la interfase. La fuerte no linealidad de las ecuaciones de gobierno impide la obtención de soluciones analíticas requiriendo, en consecuencia, técnicas numéricas para alcanzar soluciones aproximadas; en este sentido, el método de redes ha demostrado ser una herramienta precisa y eficaz proporcionando soluciones muy cercanas a las obtenidas experimentalmente con tiempos de computación aceptables y sin necesidad de introducir hipótesis que simplifican las ecuaciones de gobierno. Los problemas estudiados cubren casi todo el espectro de los procesos de corrosión: i) corrosión por dióxido de carbono, ii) corrosión por picadura, iii) corrosión a alta temperatura de compuestos de matriz metálica, iv) oxidación catalítica de gases y, v) degradación de lubricantes. Para cada tipo de oxidación anterior, del que se describe el estado del arte, se diseña el modelo en red de la celda elemental correspondiente, a partir del modelo matemático (ecuaciones de gobierno), completándose éste con las condiciones de contorno e iniciales. La simulación numérica del mismo se lleva a cabo mediante el software Pspice. Para verificar la fiabilidad de los modelos propuestos se comparan las soluciones numéricas con resultados experimentales o soluciones semianalíticas en todos los casos. Con objeto de facilitar la aplicación de los modelos propuestos se ha elaborado un programa en Matlab el cual, mediante una interfaz de comunicación gráfica y amena con el usuario, permite seleccionar el problema e introducir los parámetros que lo definen, así como generar el modelo en red, simularlo y acceder a la presentación gráfica de resultados.[ENG] In this Ph.D. the network simulation method is applied for the numerical solution of chemical oxidation problems, studying all the aspects of the phenomenon, particularly those chemical reactions processes related to the interface. The strong non-linearity of the governing equations prevents of reaching analytical solutions and requires, as a consequence, numerical techniques to provide approximate results. In this sense, network simulation method has demonstrated to be an efficiency and accurate tool that leads to numerical solution close to the experimental results with suitable computational times and without the need of assuming simplified hypotheses in the governing equations. The problems studied in this memory cover the whole spectrum of the corrosion processes: i) corrosion cause by carbon dioxide, ii) pitting corrosion, iii) high temperature corrosion of metal matrix composite, iv) catalytic oxidation of gasses and, v) lubricant degradation. For those types of oxidation, for which the state of art is introduced, the network model of the corresponding elementary volume is designed from the mathematical model (governing equations), completing this with the suitable boundary and initial conditions. Numerical simulation is carried out by means of the code Pspice. To verify the reliability of the proposed models, numerical solutions are successfully compared with those obtained experimental or semi-analytically in all the cases. In order to facilitate the application of the proposed models, suitable software has been presented as an added subject of this memory. Using a graphical and friendly communication interface, the user can select the problem and introduce the list of parameter values; this generates the complete network model, runs it in Pspice and shows graphically the simulation results.Universidad Politécnica de CartagenaPrograma de doctorado en Tecnologías Industriale

Aplicación del método de redes a la solución de problemas de fricción seca: superficies suaves a escala atómica y superficies a escala macroscópica

[ESP] El estudio del fenómeno cotidiano que supone la fricción sigue manteniendo un gran nivel de dificultad a pesar de su larga historia. Las causas de esta dificultad radican en las diferentes escalas de las características del fenómeno, macroscópicas y microscópicas, y en su distinto comportamiento en condiciones estáticas y dinámicas. A lo mencionado anteriormente se añade que los sistemas sujetos a fricción son muy sensibles al valor de los parámetros que los definen, pudiendo dar lugar a comportamientos caóticos. Así, han ido apareciendo modelos muy diferentes, válidos en un ámbito reducido, y que utilizan simplificaciones importantes que impiden su generalización. En esta tesis se presenta la aplicación del método de simulación por redes a la solución numérica al estudio de la fricción a escalas muy distintas. Por un lado, a escala microscópica se han estudiado los modelos de Frenkel-Kontorova-Tomlinson y de diferentes microscopios de fuerza atómica, relacionados con el análisis de superficies suaves a escala atómica. Por otro lado, a escala macroscópica se han estudiado los modelos relacionados con el análisis de superficies industriales, como el de un mecanismo de freno. Tras presentar en esta memoria una revisión de las distintas formulaciones de la fuerza de fricción, de la naturaleza de las superficies que participan en el fenómeno, así como de la definición de los problemas a analizar (Capítulo 2); se revisan las herramientas relacionadas con el análisis de la estabilidad de los sistemas dinámicos (Capítulo 3). En este sentido, cabe resaltar la utilidad de los diagramas de fase y los exponentes de Lyapunov, incluyendo los algoritmos más recientes para su estimación. El diseño de los modelos en red y la implementación de las condiciones iniciales se explica en el Capítulo 4. Se ha elaborado un programa en Matlab para la generación de modelos en red, simulación en Pspice y representación gráfica de resultados. En el Capítulo 5 se presenta el resultado de la aplicación de los modelos en red a los problemas planteados en el Capítulo 2. Con el fin de verificar la fiabilidad de los modelos propuestos se comparan sus resultados con las soluciones obtenidas por otros métodos numéricos o resultados experimentales, uno de ellos a partir de un dispositivo desarrollado durante la elaboración de esta memoria. [ENG] The study of everyday phenomena involving friction continues to maintain a high level of difficulty despite its long history. The causes of this problem lie in the different scale of the characteristics of the phenomenon, macroscopic and microscopic, and their different behaviour in static and dynamic conditions. To the above is added to the systems subject to friction are very sensitive to the value of the parameters that define them, may lead to chaotic behaviour. Thus, very different models, valid in a narrow scope and using simplifications that prevent generalization, have been appearing. This thesis presents the application of network simulation method to the numerical solution to the study of friction at very different scales. On the one hand, on a microscopic scale Frenkel-Kontorova-Tomlinson and different atomic force microscopes models have been studied, related to the analysis of soft surfaces at the atomic scale. Furthermore, on a macroscopic scale models related to the analysis of industrial areas, such as a brake mechanism have been studied. After presenting herein is a review of the different formulations of the friction force, the nature of the surfaces involved in the phenomenon, as well as the definition of the problems to be analyzed (Chapter 2); reviews the tools related to stability analysis of dynamic systems (Chapter 3). In this regard, we highlight the usefulness of the phase diagrams and Lyapunov exponents, including recent algorithms for their estimation. The design of network models and the implementation of the initial conditions is explained in Chapter 4. It has developed a program in Matlab to generate network models, Pspice simulation and graphical representation of results. Chapter 5 presents the result of the application of network models to problems in Chapter 2. In order to verify the reliability of the proposed models, their results are compared with the solutions obtained by other numerical methods or experimental results, one from a device developed during the preparation of this report.Universidad Politécnica de Cartagen